Question

@IMStuck Happy 4th of July!
I have more composite functions :(

Answer 1

do you mind if i help you?

Answer 2

Of course not, I would love your help :)

Answer 3

this is same as : f(g(x)) --> this means that dependent variable of function g(x) will be the independent variable of the function f(x).

So first thing that we can do is solve for g(10) or put g(x) inside f(x). which way do you want?

Answer 4

solve for g(10)

Answer 5

I find, if I may chime in, not to combine the functions but to rather, if they ask you to evaluate \[\Large (f(g(some~number))\] to evaluate \[\Large g(some~number)\] and then take that result and put it into f(x)

Answer 6

\(g(x)=x+4\\g(10)=10+4\\g(10)=?\)

what will you get?
(let's do it step by step)

Answer 7

sorry not plus, should be "-"

Answer 8

6 ! :)

Answer 9

yay right!

Then, let's put this value into the function f(x).
\(f(x)=x^2+1\\x=g(10)=4\\f(4)=x^2+1\\f(4)=4^2+1\\f(4)=?\)

did you understand the steps?

Answer 10

@Data_LG2 17

Answer 11

oops sorry again, i made a mistake it should be \(\LARGE 6\) not 4. Sorry.
\(\LARGE f(6)=6^2+1\)

Answer 12

37 @Data_LG2

Answer 13

My final answer is 37?

Answer 14

yes :)

since we are doing f(g(10)), where g(10)=6, so f(g(10))=f(6)=37

Answer 15

Thank you :)